Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x-3y &= 6 \\ -5x+y &= 1\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-5x = -y+1$ Divide both sides by $-5$ to isolate $x$ $x = {\dfrac{1}{5}y - \dfrac{1}{5}}$ Substitute this expression for $x$ in the first equation. $4({\dfrac{1}{5}y - \dfrac{1}{5}}) - 3y = 6$ $\dfrac{4}{5}y - \dfrac{4}{5} - 3y = 6$ Simplify by combining terms, then solve for $y$ $-\dfrac{11}{5}y - \dfrac{4}{5} = 6$ $-\dfrac{11}{5}y = \dfrac{34}{5}$ $y = -\dfrac{34}{11}$ Substitute $-\dfrac{34}{11}$ for $y$ in the top equation. $4x-3( -\dfrac{34}{11}) = 6$ $4x+\dfrac{102}{11} = 6$ $4x = -\dfrac{36}{11}$ $x = -\dfrac{9}{11}$ The solution is $\enspace x = -\dfrac{9}{11}, \enspace y = -\dfrac{34}{11}$.